


taxicab geometry

by orphan_account



Category: 19天 - Old先 | 19 Days - Old Xian
Genre: Alternate Universe - Canon Divergence, Developing Relationship, M/M, Multivariable Calculus, gratuitous explanations of mathematical concepts
Language: English
Status: Completed
Published: 2019-11-12
Updated: 2019-11-12
Packaged: 2021-02-01 06:07:35
Rating: Teen And Up Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 1,303
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/21410569
Author URL: https://archiveofourown.org/users/orphan_account/pseuds/orphan_account
Summary: This story is part of the LLF Comment Project (including the LLF Comment Builder), which was created to improve communication between readers and authors. This author invites and appreciates responses, including:Short commentsLong commentsQuestions“<3” as extra kudosReader-reader interactionThis author replies to comments.
Relationships: He Tian/Mo Guan Shan
Comments: 5
Kudos: 79





	taxicab geometry

Math is He Tian’s worst subject. 

Guan Shan knows it’s not because he’s bad at it. Far from it. He’s so good at it that he can’t explain it to ordinary people, people who don’t find the beauty in numbers.

It’s storming outside, cascading lightning momentarily shooting startling white blitzes through the blinds. Thunder racks through Guan Shan’s body. Starting comes too easy to him these days. He centers himself on He Tian’s nerdiness, the thunder washing off of the threatening bulk of his shoulders, the effect of worrisome weather nothing but a distraction.

“I can sum this sheet up no problem.”

He says this with the same smugness that makes their teachers shut up, makes the boys want to kill him and the girls want to fuck him and maybe also kill Guan Shan. Whenever he answers a question that way, Guan Shan stares at him.

“It’s completely valid to have your basis vectors look like they’re basic vectors,” he says, staring at Guan Shan and pointing to nonsense on the sheet.

To Guan Shan, it’s a meaningless jumble of numbers. How anyone can make sense of it, find the meaning and beauty in it, twists his gut into incurably constipated knots. There’s a word for this, an aversion to all things mathematics; his mother often reminds him of his father’s own struggles, how she helped him with the restaurant’s finances. Guan Shan doesn’t begrudge his father for this inheritance.

“They don’t have to be orthogonal to be basis vectors,” He Tian is saying, now focusing intently on the sheet. “The best way to reach any vector space is orthogonally. These aren’t orthogonal, though.”

He points to a series of numbers near the bottom of the sheet, and Guan Shan nods, steeling himself against the sting of bile rising up his throat.

“These numbers, they’re like 1 and 1.0001.”

_ What are you saying. _Why does he make it sound so fucking easy. Guan Shan knows for a fact He Tian barely studies, yet always manages to get near perfect scores on any test he considers a fuckup. An A- means binge drinking while chainsmoking through a wuxia drama. A B means a two-day bender and texting Guan Shan going on four on a Monday morning.

“_Now _ we’re thinking of polynomials.” He Tian’s flipped the sheet over to the other side. Guan Shan catches himself before burping up an embarrassing mouthful of acid. They’ve completed exactly nothing. He hasn’t thought of shutting He Tian up once. 

“Think of these polynomials as numbers with orthogonal components. That’s the only way you’ll get through this section.” He Tian stares at him hard. That’s the keen, predatory glower he’d reserved for ensnaring him in a kiss. 

Guan Shan says, “Is this where I use the Chevychev function?”

The ridiculously complex function with the equally ridiculous name that He Tian had taught him in the corridor after English, kneading his hand into Guan Shan’s neck with the greedy assurance that every passerby learned of their bond: a noble bound to a red-haired captive.

“Course you fucking can.” And here, Guan Shan smarts, the constipation loosening into an ejection of poison. Smiling, bright pools of lust cooling in his eyes, He Tian gnaws on the chewed wood of his American brand pencil. It’s the stare that reveals nothing but assumptions of untruths. That he dominates Guan Shan’s head, that his methods prove unforgettable. That they’re of any use to anyone besides him.

His voice a low purr, he says, “Forget about them for a while.” 

Scraping the chair back away from the kitchen table, Guan Shan folds his arms in a steadfast shelter around his stomach. Scowling, he punts the table with the sticky bottom of his smudged white sneaker.

“As if I could fucking keep them in my head. You were talking about dot products at lunch today.”

“You’re right.” The smugness briefly vanishes from his face, and for the span of a flickering frame in a silent film, He Tian’s a stranger to him (not that he isn’t already), a bewildered portrait of a dawning comprehension that he means something to someone. “I’m astonished you remember that.” 

Guan Shan snorts. “I don’t fucking understand you when you gab on about that shit, but I listen.”

Dangling his pencil from the side of his mouth, He Tian says, “You keep it all buried in a minefield till it blows up.” 

_ Okay, enough, asshole. You’re not my therapist. _

“So, dot vectors. They’re the sub function of the inner product, a function that takes two turns from the vector space V.” Crossing one restless leg over the other, sliding the pencil between two long fingers, He Tian lowers the heavy lids of his eyes. “Remember what V does?”

“V satisfies axioms.”

“Excellent.”

_ How the fuck do I remember that, outta all the shit he said. _

“So, for the moment, let’s imagine a series of numbers, except they’re arrows in space. Like, .000011 into infinity.”

Instead Guan Shan imagines He Tian on top of him, burying him into his bed, sucking on his ass with all of the gluttonous lust a king reserves for a concubine.

“So rather than having a conventional x and y,” He Tian is saying, “let’s picture an x and something very similar to an x.”

_ No_, Guan Shan says, with unerring confidence, in his head. _ Let’s picture you fucking me_. _ I don’t want to say no right now_. _ We’re not fifteen __anymore. _

“This right here,” and He Tian’s lost him; he’s so far beyond him and his head’s filled with the impossible beauty of numbers. He’s so far away from him and Guan Shan can’t imagine how he’d respond if he voiced his thoughts now.

“They’re talking about linear space. It’s not linear at all, that’s the trick; there are infinite ways to describe a space.” And he fights an unbearable nausea clawing at his throat as it dawns on him; he won’t shut He Tian up because if he stops talking, he might kiss him.

Through a yawn, shaking shaggy ends of dark hair between his fingers, He Tian says, “Taxicab geometry isn’t the best metric system of distance for vector shit.”

_ Maybe it’s ‘cause you’re so fucking good at something I can never hope to understand. Maybe that’s why I can’t fucking go through one day without wondering whether I wanna be you or if I wanna fuck you. No. I want _ you _ to fuck me. Now. _

“So,” He Tian says, “multivariable calculus.” 

Swearing, Guan Shan scratches shredded nails through his pale hair.

“What about it.”

“The square root of x squared.” Bending forward, Guan Shan follows the pathway of He Tian’s bony finger along the worksheet’s last set of problems.

“Plus y squared.” 

Nodding, Guan Shan leans on his elbows, obscuring half of the problem. Sharp, a fog over the quiet of the kitchen, He Tian’s scent envelopes him, an elixir for his longing.

“And now, you’ve got delta cubed plus delta y cubed plus 10 to the 1.”

Walking his fingers forward, Guan Shan allows himself a soft smirk. He tilts his head, chewing on his upper lip.

Glowering, He Tian says, “I take it you’re done.”

For the first time in a horrifically long while, Guan Shan laughs.

“Maybe if I kiss you, we’ll finally come to some fucking understanding.”

Menacing, He Tian shoves the kitchen table onto its side. 

“That’s how we’re operating, huh.”

Yanking him onto his lap, sucking back a curse as He Tian traps him against the back of the chair, Guan Shan bites his words down his neck.

“Why don’t you walk me through the order of our operation, fucking nerd.”

He Tian scoffs. “Remind me to talk about multivariable calculus with you more often.”

They don’t stop talking until four in the morning.

**Author's Note:**

> This story is part of the LLF Comment Project (including the LLF Comment Builder), which was created to improve communication between readers and authors. This author invites and appreciates responses, including:  
Short comments  
Long comments  
Questions  
“<3” as extra kudos  
Reader-reader interaction  
This author replies to comments.


End file.
